Kinetic Compressed Quadtrees in the Black-Box Model with Applications to Collision Detection for Low-Density Scenes

  • Mark de Berg
  • Marcel Roeloffzen
  • Bettina Speckmann
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7501)


We present an efficient method for maintaining a compressed quadtree for a set of moving points in ℝd. Our method works in the black-box KDS model, where we receive the locations of the points at regular time steps and we know a bound dmax on the maximum displacement of any point within one time step. When the number of points within any ball of radius dmax is at most k at any time, then our update algorithm runs in O(nlogk) time. We generalize this result to constant-complexity moving objects in ℝd. The compressed quadtree we maintain has size O(n); under similar conditions as for the case of moving points it can be maintained in O(n logλ) time per time step, where λ is the density of the set of objects. The compressed quadtree can be used to perform broad-phase collision detection for moving objects; it will report in O((λ + k)n) time a superset of all intersecting pairs of objects.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Mark de Berg
    • 1
  • Marcel Roeloffzen
    • 1
  • Bettina Speckmann
    • 1
  1. 1.Dept. of Computer ScienceTU EindhovenThe Netherlands

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